Computation of traveling waves for spatially discrete bistable reaction-diffusion equations (Q1917450)

The authors analyze an idealized system of bistable reaction-diffusion equations with spatial domain \(Z^n\), \(n=1,2,3\). The equations for traveling wave solutions are derived. These equations have the form of differential difference two-point boundary problems defined on the real line. Using an idealized nonlinear term, the lattice induced anisotropy is analyzed. Numerical methods for computing the traveling waves directly are presented. They include the use of monotone interpolants for a collocation scheme, the use of asymptotic boundary conditions and a phase condition. Finally, some numerical experiments are presented.